How is possible to create a tetrakaidecahedron? How can I keep only the edges?
Under the user preferences make sure you activate the default bundled addon Add Mesh Extra Objects.

Add a new mesh of the type Math Function > Regular Solid and from the presets at the bottom pick Truncated Octahedron.

Erase the edges dividing the large faces in half, then add a Wireframe modifier.

Adjust the thickness as desired and add two Subdivision modifiers below it. The top one must be set to Simple, and the second one to Catmull-Clark.

Adjust subdivisions as desired for a more organic or geometric look.